#include <bits/stdc++.h>
using namespace std;
typedef signed long long ll;

#define _P(...) (void)printf(__VA_ARGS__)
#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define FORR2(x,y,arr) for(auto& [x,y]:arr)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
template<class T> bool chmax(T &a, const T &b) { if(a<b){a=b;return 1;}return 0;}
template<class T> bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;}
//-------------------------------------------------------

int N,M;
int B[2020];
const ll mo=998244353;

ll comb(ll N_, ll C_) {
	const int NUM_=400001;
	static ll fact[NUM_+1],factr[NUM_+1],inv[NUM_+1];
	if (fact[0]==0) {
		inv[1]=fact[0]=factr[0]=1;
		for (int i=2;i<=NUM_;++i) inv[i] = inv[mo % i] * (mo - mo / i) % mo;
		for (int i=1;i<=NUM_;++i) fact[i]=fact[i-1]*i%mo, factr[i]=factr[i-1]*inv[i]%mo;
	}
	if(C_<0 || C_>N_) return 0;
	return factr[C_]*fact[N_]%mo*factr[N_-C_]%mo;
}

void solve() {
	int i,j,k,l,r,x,y; string s;
	
	cin>>N>>M;
	FOR(i,N) cin>>B[i];
	
	ll ret=0;
	for(i=0;i<=M;i++) {
		int C[4];
		FOR(j,N) {
			C[j]=B[j]-i;
			if(C[j]<0) break;
		}
		if(j<N) continue;
		int a=C[0],b=C[3];
		if(a+b+i>M) continue;
		ll pat=comb(M,i)*comb(M-i,a)%mo*comb(M-i-a,b)%mo;
		for(int p1=0;p1<=min(a,C[1]);p1++) {
			int p2=C[2]-(C[1]-p1);
			if(p2<0) {
				p1+=-p2-1;
				continue;
			}
			if(p2>b) {
				break;
			}
			ret+=pat*comb(a,p1)%mo*comb(b,p2)%mo*comb(a-p1+b-p2,C[1]-p1)%mo;
		}
	}
	cout<<ret%mo<<endl;
	
}


int main(int argc,char** argv){
	string s;int i;
	if(argc==1) ios::sync_with_stdio(false), cin.tie(0);
	FOR(i,argc-1) s+=argv[i+1],s+='\n'; FOR(i,s.size()) ungetc(s[s.size()-1-i],stdin);
	cout.tie(0); solve(); return 0;
}